what you quote isn't evidence that the US is against immigrating British citizens. It just means that some British citizens find it difficult to immigrate to the US.
Really the same laws apply to British citizens than to any other citizens. Actually the fact that they can't participate in the greencard lottery is proof that it isn't particularly difficult for them. Because it means that there are already a lot of British citizens immigrating to the US, so they are not underrepresented among immigrants, so they can't participate in the greencard lottery. The official name of the greencard lottery is diversity visa lottery. A country is only eligible for the greencard lottery if not more than 50,000 immigrants to the United States in the previous five years have come from this country.
The "proof" you provided is true for all people around the world. Who gives out jobs to anyone without ever meeting in person? Actually, people of some countries are more favored, as they are able to walk into America and go for an interview if needed. Unfortunately, others are not so lucky. Why is it so hard to find an employer, especially if you visit the country often? And once you are employed you will be soon in a position to establish your permanent residency.
At that time don't forget the plight of the likes of us Indians and Chinese, who presently have ZERO hope of ever making it, even if they have jobs!